Contour overheating and idle problem

Can't say specifically about your car but Ford does have way more trouble with coolant temperature sensors than all other brands combined. It's actually fairly common. As for the connector, it's rare to have one that you can't pick the terminals to tighten them so they make better contact if they're loose, but it will have to be replaced if the terminals are corroded. Chrysler has replacement terminals for all of their connectors. GM has their kits too but like all GM parts they are very expensive. I would be surprised if Ford doesn't have similar repair kits. Also, the auto parts stores have entire catalogs of just replacement connectors for every imaginable car brand and model. I prefer snipping them off of cars in the salvage yard. You'll end up with the same thing as a new connector and it should work fine if it wasn't previously damaged by rough handling or corrosion.